On the Complexity of Slide-and-Merge Games Ahmed Abdelkader, Aditya - PowerPoint PPT Presentation

Sep 26, 2022 •210 likes •288 views

On the Complexity of Slide-and-Merge Games Ahmed Abdelkader, Aditya Acharya, Philip Dasler Slide and Merge Games Slide tiles in a NxN grid Equal valued tiles merge Objective: To produce a tile of a given target value Related Work

On the Complexity of Slide-and-Merge Games Ahmed Abdelkader, Aditya Acharya, Philip Dasler
Slide and Merge Games ● Slide tiles in a NxN grid ● Equal valued tiles merge ● Objective: To produce a tile of a given target value
Related Work ● Push-1: A block pushing puzzle ● Move to the target location by pushing blocks ● PushPush: Blocks slide all the way ● Shown to be NP-Hard [Demaine et al. 2000]
Related Work ● Bejeweled and Candy Crush: ● Match three similar three tiles to make them disappear ● Objective: to create as many matching as possible ● Shown to be NP-Hard [Guala et al. 2014]
2048 ● Like tiles merge ● All pieces slide as far as possible ● All single merges that can happen, will ● New tiles ∈ {2,4} are added randomly ● Objective: Obtaining a tile of value 2048
Reduction Approaches • Bejeweled, Candy Crush shown to be NP- Hard: reduction from 1-in-3 Positive SAT • Clauses encoded by a pattern of tiles, satisfied by clearing those tiles • Assignments of variables encoded by the choice of tiles to merge
Reduction Approaches • Push is NP-Hard in 3D [ Rourke 1999] by a reduction from SAT • Push in 2D: • Similar approach to reduction in 3D • Extra gadgets to take care of path intersection

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